Functional calculus for non-commuting operators with real spectra via an iterated Cauchy formula

We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators A_j on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also extended to tuples of more general operators allowing smooth functional calculii. We also discuss the relation to the case with commuting operators.     

The Orevkov invariant of an affine plane curve

We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the Orevkov invariant.

     

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Best affine unbiased representations of the fully restricted general Gauss-Markov model

This article completes and simplifies earlier results on the derivation of best linear, or affine, unbiased estimates in the general Gauss-Markov model with a singular dispersion matrix and additional restrictions under very general conditions. We provide the class of all linear representations of the best affine unbiased estimator with precise statements concerning its indeterminacy.